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Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Question 11
Triangle T is drawn on a coordinate grid. (a) Translate triangle T using the vector $\begin{pmatrix} -3 \\ 1 \end{pmatrix}$. (b) Describe fully the single transfor... show full transcript
Worked Solution & Example Answer:Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Step 1
Translate triangle T using the vector $\begin{pmatrix} -3 \\ 1 \end{pmatrix}$
Answer
To perform the translation, each vertex of triangle T is moved according to the vector. This means:
- For a vertex at coordinates , the new coordinates after translation will be .
Thus, if the original vertices of triangle T are known, substitute those values into the transformation.
Step 2
Describe fully the single transformation that represents the following.
Answer
For (i) A rotation with centre (0, 0) of 180° followed by a rotation with centre (0, 0) of 90° clockwise:
- The 180° rotation will reflect the triangle through the origin, resulting in new positions of the vertices. After the rotation, the triangle is oriented in the opposite direction.
- Following this, the rotation of 90° clockwise will move all points one quarter turn around the origin.
The combined effect can be described by stating that this is a single rotation about the origin of 90° clockwise, with the initial position of the vertices being the result of the 180° rotation.
For (ii) A reflection in the x-axis followed by a reflection in the y-axis:
- The reflection in the x-axis will change the y-coordinates of each vertex to their negatives.
- The subsequent reflection in the y-axis will change the x-coordinates of each vertex to their negatives.
This transformation can be seen as a rotation of 180° about the origin, effectively swapping the positions of the triangle across both axes.